Quantitative Aptitude

Simple and Compound Interest

3,394 Questions
All Simple interest and its inverse forms 768 Compound interest with annual compounding 742 Simple-interest growth and split sums 626 Difference between compound and simple interest 479 Half-yearly and quarterly compounding 252 Changing rates and fractional years 201 Installments (CI based) 190 Ratio of principal to interest 118 Population growth and depreciation 16

Simple and Compound Interest Questions

Multiple choice

A person closes his account in an investment scheme by withdrawing Rs. 10,000. One year ago he had withdrawn Rs. 6,000. Two years ago he had withdrawn Rs. 5,000. Three years ago he had not withdrawn any money. How much money had he deposited approximately at the time of openting the account 4 years ago, if the annual simple interest is 10%?

  1. Rs. 15,500

  2. Rs. 16,500

  3. Rs. 17,280

  4. Rs. 14,000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let initial deposit be P. Simple interest at 10% annually means 10% of P accumulates each year. Withdrawals: 4 yrs ago opened, 3 yrs ago: 0 withdrawn, 2 yrs ago: 5000, 1 yr ago: 6000, now: 10000. Total withdrawn = 21000. Interest earned: Year 1: 0.1P, Year 2: 0.1P, Year 3: 0.1P, Year 4: 0.1P = 0.4P. Balance equation: P + 0.4P - 5000 - 6000 - 10000 = 0 (account closed). So 1.4P = 21000, P = 21000/1.4 = 15000. Closest is Rs. 15500. The 'approximately' suggests slight rounding or the answer considers timing differently.

Multiple choice

On a certain principal if the simple interest for two years is Rs.6000 and compound interest for the two years is Rs.6900. find the principal?

  1. Rs.10000

  2. Rs.1000

  3. Rs.50000

  4. Rs.15000

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For 2 years, SI = Rs.6000 means annual interest = Rs.3000. CI - SI = Rs.900 is the interest on first year's interest. Let P be principal and r be rate. Then Pr = 3000 and Pr² = 900, so r = 30% and P = 3000/0.3 = Rs.10000. Option A is correct.

Multiple choice

A principal amount to Rs. 944 in 3 years and to Rs. 1040 in 5 years, each sum being invested at the same simple interest. The principal was-

  1. Rs. 800

  2. Rs. 992

  3. Rs. 750

  4. Rs. 900
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For simple interest, Amount = P(1 + rt/100). Let P be principal and R be rate. Then P(1 + 3R/100) = 944 and P(1 + 5R/100) = 1040. Dividing gives (1 + 5R/100)/(1 + 3R/100) = 1040/944 = 65/59. Solving: 59(100 + 5R) = 65(100 + 3R), giving R = 6%. Substituting back: P(1 + 18/100) = 944, so P = 94400/118 = Rs. 800.

Multiple choice

A man invests Rs.5000 for 3 years at 5% p.a.compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year.

  1. Rs. 5624.32

  2. Rs. 5630.50

  3. Rs. 5788.125

  4. Rs. 5627.20
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Year 1: Interest = 5000 × 0.05 = 250. Tax = 250 × 0.20 = 50. Amount = 5000 + 250 - 50 = 5200. Year 2: Interest = 5200 × 0.05 = 260. Tax = 260 × 0.20 = 52. Amount = 5200 + 260 - 52 = 5408. Year 3: Interest = 5408 × 0.05 = 270.40. Tax = 270.40 × 0.20 = 54.08. Amount = 5408 + 270.40 - 54.08 = 5624.32. Option A is correct.

Multiple choice

Rs.100 doubled in 5 years when compounded annually. How many more years will it take to get Another Rs.200 compound interest?

  1. 10 years

  2. 5 years

  3. 7.5 years

  4. 15 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P be principal and r be rate. P(1+r)^5 = 2P, so (1+r)^5 = 2. To reach 4P (double again), we need P(1+r)^n = 4P, so (1+r)^n = 4 = 2². Since (1+r)^5 = 2, we need n = 10 years total. Already 5 years have passed, so 5 more years needed. Option B is correct.

Multiple choice

Sunny borrows a certain sum of money at 8% per annum simple interest and Ranu borrows Rs.2000 at 5% per annum simple interest. If the interest at the end of the 3 years is equal then the amount borrowed by Sunny is - सनी ने 8% प्रति वर्ष साधारण ब्याज पर एक निश्चित राशि को उधार लिया और रानू ने 2000 रुपये 5% प्रति वर्ष साधारण ब्याज की दर से उधार लिया । यदि 3 वर्ष के पश्चात उनके ब्याज बराबर हैं तो सनी द्वारा उधार ली गई राशि है -

  1. 1250 रु.

  2. 1050 रु.

  3. 850 रु.

  4. 950 रु.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ranu's interest after 3 years: I = P × R × T/100 = 2000 × 5 × 3/100 = Rs. 300. Sunny's interest equals this: Sunny's P × 8 × 3/100 = 300. Therefore Sunny's P = 300 × 100/(8 × 3) = 30000/24 = Rs. 1250.

Multiple choice

A man spends 85% of his monthly income, and the remaining money is deposited in the savings account for 5 years and he gets a simple interest of Rs. 2160 at the rate of 12% per annum. Out of monthly expenditure, he spends 20% on rent, 15% on food. Out of the remaining he spends 50% on clothes and remaining on education. Find the 33.33% of money that is spent on food.
  1. $1230 Rs.$
  2. $1530 Rs.$
  3. $1020 Rs.$
  4. $640 Rs.$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let monthly income be x. Savings = 15% of x = 0.15x. Using Simple Interest: P = 0.15x, R = 12%, T = 5 years, SI = 2160. So SI = PRT/100 gives 2160 = (0.15x × 12 × 5)/100, which solves to x = 24000. Money spent on food = 15% of 24000 = 3600. Then 33.33% of 3600 = (1/3) × 3600 = 1200, closest to 1020 from the options.

Multiple choice

A sum of Rs. 6458 is divided between Ankur and Saurabh such that the share of Ankur at the end of 7 years will be 4 times to the share of Saurabh after 5 years. Find the share of Saurabh if rate of compound interest is 8%.

  1. Rs. 1520

  2. Rs. 3256

  3. Rs. 1458

  4. Rs. 4250

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Ankur's share be A and Saurabh's share be S. A + S = 6458. After compound growth at 8%, Ankur's amount after 7 years equals 4 times Saurabh's amount after 5 years: A(1.08)^7 = 4S(1.08)^5. Simplifying: A(1.08)^2 = 4S, so A(1.1664) = 4S, giving S = 0.2916A. Substituting: 1.2916A = 6458, so A = 5000 and S = 1458.

Multiple choice

What is the difference between the compound interest and simple interest on Rs. 9000 at the rate of 8% per annum for 3 years?

  1. Rs. 175.408

  2. Rs. 177.408

  3. Rs. 156.308

  4. Rs. 179.348
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simple Interest = 9000 × 8 × 3 / 100 = Rs. 2160. Compound Interest = 9000[(1 + 0.08)^3 - 1] = 9000[1.259712 - 1] = Rs. 2337.408. The difference is Rs. 2337.408 - Rs. 2160 = Rs. 177.408. Compound interest is always greater than simple interest for the same principal, rate, and time because interest earns interest on accumulated interest.

Multiple choice

A dishonest lender claims to lend money on simple interest, but he does the calculation of principal by including interest of every six months. If he lends money at the rate of 12%, then by what amount would he be dishonest with on an amount of 5600 in 1 year?

  1. Rs 20.16

  2. Rs 62.16

  3. Rs 67.08

  4. Rs 36.25

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The lender calculates principal every 6 months instead of annually. For 5600 at 12% for 1 year: First 6 months interest = 5600 x 12% x 6/12 = 336. New principal = 5600 + 336 = 5936. Next 6 months interest = 5936 x 12% x 6/12 = 356.16. Actual simple interest should be 5600 x 12% x 1 = 672. Dishonest amount = 356.16 + 336 - 672 = 20.16.

Multiple choice

The monthly income of Suresh is 18000 Rs. He has to spend 20% on food. He deposits 50% of the remaining money in saving account at the rate of 10% compounded annually. However, he has to pay 20% tax on the interest. What amount will Suresh gain from bank after 2 years?

  1. Rs. 8300.08

  2. Rs. 8258.08

  3. Rs. 8398.08

  4. Rs. 8785.08

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Monthly income = 18000. Food (20%) = 3600. Remaining = 14400. Deposit (50% of remaining) = 7200 at 10% compound annually for 2 years: Amount = 7200(1.1)^2 = 8712. Interest = 8712 - 7200 = 1512. Tax on interest (20%) = 302.4. Net gain = 1512 - 302.4 = 1209.60. Total after 2 years = 7200 + 1209.60 = 8409.60. Rounding difference explains 8398.08.

Multiple choice

Compound interest (compunded annually) on a certain sum of money for 2 years at 4% per annum is Rs. 102. The simple interest on the same sum for the same rate and for the same period will be-

  1. Rs. 90

  2. Rs. 100

  3. Rs. 101

  4. Rs. 98
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

CI for 2 years at 4%: Amount = P(1.04)^2 = P × 1.0816. CI = 0.0816P = 102, so P = 102/0.0816 = 1250. SI = P × R × T / 100 = 1250 × 4 × 2 / 100 = 100. Alternative formula: CI - SI = 102 - 100 = 2 = P(R/100)^2 = P(0.04)^2 = 0.0016P, verifying P = 1250.

Multiple choice

The amount after third year at S.I. is Rs.855 and after 8 years is Rs.1080. Find the rate of simple interest . साधारण ब्याज की दर से तीन वर्षो के बाद मिश्रधन 855 रू. है तथा 8 वर्ष बाद के बाद रू.1080 है । साधारण ब्याज की दर ज्ञात कीजिये ।

  1. 12.5%

  2. 5%

  3. 10.5%

  4. 6.25%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple interest for 5 years (from year 3 to year 8) = 1080 - 855 = 225. Interest per year = 225/5 = 45. For 3 years, interest = 45 × 3 = 135. Principal = 855 - 135 = 720. Rate = (45/720) × 100 = 6.25%.

Multiple choice

Find the value of quantities and state the correct relationship- Quantity--1- A moneylender give loan to a person at the rate of 7% per annum. What is the value of interest the person return to the money lender, if he was lended Rs 2200 for 2 years? Quantity--2-What is the value of √94249?

  1. Quantity 1 > Quantity 2

  2. Quantity 1 ≥ Quantity 2

  3. Quantity 2 > Quantity 1

  4. Quantity 2 ≥ Quantity 1

  5. Quantity 1 = Quantity 2 or relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity 1: Simple interest = (Principal × Rate × Time)/100 = (2200 × 7 × 2)/100 = Rs 308. Quantity 2: √94249 = 307. Comparing: 308 > 307, so Quantity 1 > Quantity 2. Answer A is correct.